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An averaged soliton occurs when a soliton propagates through a medium that is periodically heterogeneous. The reason is that the propagation in a homogeneous medium is consistent with the stability consideration of a single eigenvalue spectrum, even in the cases of loss and amplification processes. This assumption changed in tandem media where we considered local changes. In this paper, we focus on the nonlinear dynamics and show that optical solitons, both temporal and spatial, reshape into a nonlinear modulation from medium to medium when they propagate through a periodically stratified nonlinear medium. It can be locally linearized as a perturbation near the corresponding soliton eigenvalue. We analytically and numerically discuss two particular optical soliton problems to show their generality: that of a Two-Level Atom medium (TLA) and a Kerr nonlinearity as a description of those materials and photorefractive materials. We can conclude that rather than a mean soliton, we have a modulated soliton.